The 28-year-old's contract at Bayern is due to expire at the end of June, and he will be leaving the German champions this summer in search of pastures new.
Madrid have been strongly linked with the Austria international, but a switch to the Bernabeu has not yet been announced, and a number of clubs continue to be linked with his services.
The report claims that a move for Alaba has been in place since the early stages of 2021, with Madrid holding off competition from Barcelona and a number of English clubs to secure his signature.
The Austrian has again been a key player for Bayern during the 2020-21 campaign, scoring twice and providing four assists in 39 appearances in all competitions.
As it stands, Madrid captain Sergio Ramos will leave on a free transfer at the end of June, while fellow centre-back Raphael Varane continues to be linked with a move away from the club. body check tags ::